Problem 20 - Chemistry The Central Science In Si Units

Question

Which of the following statements are true and which are false? (a) For the reaction \(2 \mathrm{~A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{A}_{2} \mathrm{~B}(g) K_{c}\) and \(K_{p}\) are numerically the same. (b) It is possible to distinguish \(K_{c}\) from \(K_{p}\) by comparing the units used to express the equilibrium constant. (c) For the equilibrium in (a), the value of \(K_{c}\) increases with increasing pressure.

Step-by-Step Solution

Answer

(a) False, (b) True, (c) False.

Step 1: Understanding the Reaction

The given reaction is \(2 \mathrm{~A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{A}_{2} \mathrm{~B}(g)\). This is a gaseous reaction where 2 moles of gas A and 1 mole of gas B react to form 1 mole of \(\mathrm{A}_{2}\mathrm{~B}\).

Step 2: Relation Between Kc and Kp

The relationship between \(K_c\) and \(K_p\) for a gaseous reaction is given by the equation: \[ K_p = K_c (RT)^{\Delta n} \] where \(\Delta n\) is the change in the number of moles of gas. For the given reaction, \(\Delta n = 1 - (2+1) = -2\). So, \( K_p eq K_c \) unless \( RT \) raised to the power \(-2\) is equal to 1, which generally only happens under specific condition of temperature or pressure.

Step 3: Units of Kc and Kp

\(K_c\) is expressed in terms of concentration (mol/L) while \(K_p\) is expressed in terms of pressure (atm or Pa). Therefore, the units of \(K_c\) and \(K_p\) are different due to their dependence on concentration and pressure respectively, allowing one to distinguish between them.

Step 4: Effect of Pressure on Kc

\(K_c\) is calculated from concentration only; hence, it is independent of pressure. An increase in pressure changes the concentrations of the components but does not affect \(K_c\). Therefore, \(K_c\) remains unchanged with a change in pressure.

Key Concepts

Equilibrium Constants

In chemistry, equilibrium constants play a crucial role in understanding chemical equilibrium. They are numerical values that describe the balance between the products and reactants in a reversible chemical reaction at equilibrium. This concept helps us predict the extent to which a reaction occurs before reaching equilibrium.
Equilibrium constants are denoted by either \( K_c \) or \( K_p \).

• \( K_c \) refers to equilibrium constants expressed in terms of concentration (molarity).
• \( K_p \) refers to equilibrium constants expressed in terms of partial pressures of gases.

Each constant offers insights into the position of equilibrium. A larger equilibrium constant indicates a greater concentration of products at equilibrium, suggesting the reaction strongly favors the formation of products. Conversely, a smaller constant implies more reactants are present, favoring the reverse reaction.
Understanding the difference between \( K_c \) and \( K_p \) is pivotal when dealing with gaseous reactions, as they have different applications depending on the state variables that are more easily measured for the system.

Kc and Kp Relationship

The relationship between \( K_c \) and \( K_p \) reveals important details about how gases behave concerning their concentrations and pressures. For gaseous reactions, these two constants are related by the equation:\[K_p = K_c (RT)^{\Delta n}\]where:

• \( R \) is the universal gas constant.
• \( T \) is the temperature in Kelvin.
• \( \Delta n \) is the change in moles of gas, calculated as the difference between moles of products and moles of reactants.

In the given example of the reaction \( 2 \mathrm{~A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{A}_{2}\mathrm{~B}(g) \), \( \Delta n \) is calculated as \( 1 - 3 = -2 \).
This negative change implies that \( K_p \) and \( K_c \) will not generally be equivalent, unless specific conditions of temperature and pressure make \( (RT)^{-2} = 1 \). Understanding these relationships allows chemists to predict and control the conditions under which reactions are conducted, impacting both product yield and efficiency.

Gaseous Reactions

Gaseous reactions are unique due to the properties of gases, affecting how equilibrium is established. These reactions often involve changes in volume and pressure, which influence the behavior and position of chemical equilibrium.One must consider:

• The number of moles of gases involved, which is subject to change, influencing the equilibrium constant directly through \( \Delta n \).
• Pressure and volume changes that can impact the reactants and products at equilibrium.

In our given reaction, \( 2 \mathrm{~A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{A}_{2}\mathrm{~B}(g) \), even though pressure might fluctuate, \( K_c \) remains constant because it depends solely on concentrations and not on pressure. However, \( K_p \) could show variability given that it directly relates to partial pressures.
Thus, the understanding of gaseous reactions is essential, as different external conditions can lead to different outcomes in equilibrium states. This knowledge plays an integral role in industrial applications where conditions are optimized to maximize the production of desired products.